Teaching Natural Deduction as a Subversive Activity

In this paper we argue that sequent proofs systems are a better deductive apparatus for introducing proofs to students than are natural deduction systems. Natural deduction derivations of superintuitionistic theorems (theorems of classical logic that are not intuitionistically valid) require indirect and often obtuse constructions. Constructing derivations in sequent systems is uniform, driven by syntax. The strong claim often made for natural deduction is that derivations closely reflect the logical thought process. We argue here that, for the superintuitionistic theorems, classical sequent derivations also reflect a logical thought process which is more concise and more direct than their natural deduction counterparts.